Difference between revisions of "Parabolic Shot/es"
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ESTA PÁGINA ESTÁ SIENDO TRADUCIDA. TEN UN POCO DE PACIENCIA. GRACIAS. | ESTA PÁGINA ESTÁ SIENDO TRADUCIDA. TEN UN POCO DE PACIENCIA. GRACIAS. | ||
| + | == Mathematical function to follow == | ||
| + | |||
| + | We're going to simulate a cannon shot. A cannonball describes a parabolic trajectory after it is fired from the cannon. | ||
| + | |||
| + | {{l|Image:Parabolic-shot.gif}} | ||
| + | |||
| + | The mathematical equations that govern the trajectory are: | ||
| + | |||
| + | <math>X(t)=V_{0x}\cdot t+X_0</math> | ||
| + | |||
| + | <math>Y(t)=-\frac{1}{2}\cdot G \cdot t^2 + V_{0y}\cdot t + Y_0</math> | ||
| + | |||
| + | where: | ||
| + | |||
| + | <math>t</math> = the current time for the mathematical equation. | ||
| + | |||
| + | <math>X</math> = the 'x' coordinate of the bullet at a time 't' | ||
| + | |||
| + | <math>Y</math> = the 'y' coordinate of the bullet at a time 't' | ||
| + | |||
| + | <math>X_0</math> = the 'x' position of the bullet at time t = 0 | ||
| + | |||
| + | <math>Y_0</math> = the 'y' position of the bullet at time t = 0 | ||
| + | |||
| + | <math>V_{0x}</math> = the 'x' component of the velocity when shot (t = 0) | ||
| + | |||
| + | <math>V_{0y}</math> = the 'y' component of the velocity when shot (t = 0) | ||
| + | |||
| + | <math>G</math> = the gravity's acceleration. | ||
| + | |||
| + | You usually have the angle and the velocity modulus instead of its components. The decomposition is quite easy: | ||
| + | |||
| + | <math>V_{0x} = V_0 \cdot \cos \varphi</math> | ||
| + | |||
| + | <math>V_{0y} = V_0 \cdot \sin \varphi</math> | ||
| + | |||
| + | where: | ||
| + | |||
| + | <math>V_0</math> = the velocity when shot (t = 0) | ||
| + | |||
| + | <math>\varphi</math> = the cannon shooting angle with the horizontal. | ||
| + | |||
| + | See [http://en.wikipedia.org/wiki/Trajectory_of_a_projectile this Wikipedia article] if you need more information regarding the maths equations of a parabolic shot. | ||
Revision as of 10:53, 13 October 2011
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ESTA PÁGINA ESTÁ SIENDO TRADUCIDA. TEN UN POCO DE PACIENCIA. GRACIAS.
Mathematical function to follow
We're going to simulate a cannon shot. A cannonball describes a parabolic trajectory after it is fired from the cannon.
The mathematical equations that govern the trajectory are:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle X(t)=V_{0x}\cdot t+X_0}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle Y(t)=-\frac{1}{2}\cdot G \cdot t^2 + V_{0y}\cdot t + Y_0}
where:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle t} = the current time for the mathematical equation.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle X} = the 'x' coordinate of the bullet at a time 't'
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle Y} = the 'y' coordinate of the bullet at a time 't'
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle X_0} = the 'x' position of the bullet at time t = 0
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle Y_0} = the 'y' position of the bullet at time t = 0
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_{0x}} = the 'x' component of the velocity when shot (t = 0)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_{0y}} = the 'y' component of the velocity when shot (t = 0)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle G} = the gravity's acceleration.
You usually have the angle and the velocity modulus instead of its components. The decomposition is quite easy:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_{0x} = V_0 \cdot \cos \varphi}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_{0y} = V_0 \cdot \sin \varphi}
where:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle V_0} = the velocity when shot (t = 0)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \varphi} = the cannon shooting angle with the horizontal.
See this Wikipedia article if you need more information regarding the maths equations of a parabolic shot.
